{"id":"W193848668","doi":"10.1007/978-1-4612-1206-5_20","title":"Painlevé—Calogero Correspondence","year":2000,"lang":"en","type":"book-chapter","venue":"","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":27,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"","keywords":"Hamiltonian system; Hamiltonian (control theory); Phase space; Mathematics; Mathematical physics; Affine transformation; Elliptic curve; Riemann hypothesis; Mathematical analysis; Integrable system; Pure mathematics; Elliptic function; Physics; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002398684,0.0006552837,0.0004875951,0.001576195,0.001937696,0.002666659,0.0006925595,0.001886255,0.06160911],"category_scores_gemma":[0.001017167,0.0002732289,0.0002167155,0.001170237,0.001674709,0.003188664,0.001441405,0.002944652,0.02228956],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002373114,"about_ca_system_score_gemma":0.0005852464,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001971172,"about_ca_topic_score_gemma":0.003510651,"domain_scores_codex":[0.9997932,0.00003007941,0.000005677555,0.00005748758,0.00008328836,0.00003022802],"domain_scores_gemma":[0.9998395,0.00004582075,0.00001342152,0.00002842756,0.00005152311,0.00002123231],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001303908,0.00001239845,0.00002141496,0.00003955615,0.000002730954,0.00004657152,0.00008663083,0.0001209245,0.0001225379,0.8412997,0.1324784,0.02575611],"study_design_scores_gemma":[0.000005122139,0.000004417695,0.00008353437,0.00003334056,0.000002176585,0.0001121857,0.00003273163,0.0001985822,0.000151254,0.1882893,0.8110821,0.000005297075],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.0007170144,0.004437958,0.001907143,0.00443278,0.002143024,0.000009921775,0.00007622252,0.00006739559,0.9862087],"genre_scores_gemma":[0.02107287,0.003168595,0.0007926651,0.001114968,0.001537178,0.00002626482,0.0000735972,0.0001058864,0.9721079],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.06160911,"threshold_uncertainty_score":0.206103,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01284545847522038,"score_gpt":0.2342407175285345,"score_spread":0.2213952590533141,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}